You are asking the wrong question. The right question you should be asking yourself is "How do I best explain what I want to say, to the audience I have identified for the thing I'm writing". You will notice that I'm saying this not with regard to a research statement as part of an application, but in general: This is the advice you should consider for everything you write: Identify who your audience is, what they know, what they want to get out of what you are writing for them, and then use that insight to decide how you should write.
As for the specific question: Yes, research statements addressed to math departments typically use formulas. That's because that audience is clearly capable to understand these formulas, and will want to see enough detail that it is worth stating them in concise, mathematical notation.